How do you find the slope of the tangent line to the graph of $f(x)=-x^2+4sqrt(x)$ at x = 4?

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Answer 1 · 2015-03-25T16:20:02

The answer is: $-7$ .

The slope of the tangent line to the grapf of $f(x)$ in $x=a$ is:

$m=f'(a)$ .

So:

$y'=-2x+4/(2sqrtx)=-2x+2/sqrtx$ , and:

$y'(4)=-2*4+2/sqrt4=-8+1=-7$ .

How do you find the slope of the tangent line to the graph of f(x)=-x^2+4sqrt(x)f(x)=-x^2+4sqrt(x) at x = 4?